NRICH: Square Grid

Can you work out what fraction of this grid is shaded?

A square is split into a 100 by 100 square grid.

100 squares in the first row are shaded, 99 in the second row, 98 in the third row, and so on.

What fraction of the whole square is shaded?

This problem is taken from the World Mathematics Championships

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Age 11 to 14


Algebra & Pre-Algebra, Fractions & Decimals, Patterning & Sequencing
Middle School, High School

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NRICH (University of Cambridge)

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